TurbulenceClosures

TurbulenceClosures

Functions for turbulence, sub-grid scale modeling. These include viscosity terms, diffusivity and stress tensors.

• ConstantViscosity
• ViscousSponge
• SmagorinskyLilly
• Vreman
• AnisoMinDiss

TurbulenceClosureModel

Abstract type with default do-nothing behaviour for arbitrary turbulence closure models.

WithDivergence

A divergence type which includes the divergence term in the momentum flux tensor

WithoutDivergence

A divergence type which does not include the divergence term in the momentum flux tensor

ConstantViscosity <: TurbulenceClosureModel

Abstract type for constant viscosity models

ConstantDynamicViscosity <: ConstantViscosity

Turbulence with constant dynamic viscosity (ρν). Divergence terms are included in the momentum flux tensor if divergence_type is WithDivergence.

Fields

• ρν

  Dynamic Viscosity [kg/m/s]

• divergence_type

ConstantKinematicViscosity <: ConstantViscosity

Turbulence with constant kinematic viscosity (ν). Divergence terms are included in the momentum flux tensor if divergence_type is WithDivergence.

Fields

• ν

  Kinematic Viscosity [m2/s]

• divergence_type

SmagorinskyLilly <: TurbulenceClosureModel

Fields

• C_smag

  Smagorinsky Coefficient [dimensionless]

Smagorinsky Model Reference

See Joseph Smagorinsky (1963)

Lilly Model Reference

See Douglas K Lilly (1962)

Brunt-Väisälä Frequency Reference

See Dale R Durran , Joseph B Klemp (1982)

Vreman{FT} <: TurbulenceClosureModel

Filter width Δ is the local grid resolution calculated from the mesh metric tensor. A Smagorinsky coefficient is specified and used to compute the equivalent Vreman coefficient.

1. ν_e = √(Bᵦ/(αᵢⱼαᵢⱼ)) where αᵢⱼ = ∂uⱼ∂uᵢ with uᵢ the resolved scale velocity component.
2. βij = Δ²αₘᵢαₘⱼ
3. Bᵦ = β₁₁β₂₂ + β₂₂β₃₃ + β₁₁β₃₃ - β₁₂² - β₁₃² - β₂₃²

βᵢⱼ is symmetric, positive-definite. If Δᵢ = Δ, then β = Δ²αᵀα

Fields

• C_smag

  Smagorinsky Coefficient [dimensionless]

Reference

• AW Vreman (2004)

AnisoMinDiss{FT} <: TurbulenceClosureModel

Filter width Δ is the local grid resolution calculated from the mesh metric tensor. A Poincare coefficient is specified and used to compute the equivalent AnisoMinDiss coefficient (computed as the solution to the eigenvalue problem for the Laplacian operator).

Fields

• C_poincare

Reference

See Catherine A Vreugdenhil , John R Taylor (2018)

HyperDiffusion

Abstract type for HyperDiffusion models

NoHyperDiffusion <: HyperDiffusion

Defines a default hyperdiffusion model with zero hyperdiffusive fluxes.

DryBiharmonic{FT} <: HyperDiffusion

Assumes dry compressible flow. Horizontal hyperdiffusion methods for application in GCM and LES settings Timescales are prescribed by the user while the diffusion coefficient is computed as a function of the grid lengthscale.

Fields

• τ_timescale

EquilMoistBiharmonic{FT} <: HyperDiffusion

Assumes equilibrium thermodynamics in compressible flow. Horizontal hyperdiffusion methods for application in GCM and LES settings Timescales are prescribed by the user while the diffusion coefficient is computed as a function of the grid lengthscale.

Fields

• τ_timescale

• τ_timescale_q_tot

ViscousSponge

Abstract type for viscous sponge layers. Modifier for viscosity computed from existing turbulence closures.

NoViscousSponge

No modifiers applied to viscosity/diffusivity in sponge layer

Fields

UpperAtmosSponge{FT} <: ViscousSponge

Upper domain viscous relaxation.

Applies modifier to viscosity and diffusivity terms in a user-specified upper domain sponge region

Fields

• z_max

  Maximum domain altitude (m)

• z_sponge

  Altitude at with sponge starts (m)

• α_max

  Sponge Strength 0 ⩽ α_max ⩽ 1

• γ

  Sponge exponent

ν, D_t, τ = turbulence_tensors(
    ::TurbulenceClosureModel,
    orientation::Orientation,
    param_set::AbstractParameterSet,
    state::Vars,
    diffusive::Vars,
    aux::Vars,
    t::Real
)

Compute the kinematic viscosity (ν), the diffusivity (D_t) and SGS momentum flux tensor (τ) for a given turbulence closure. Each closure overloads this method with the appropriate calculations for the returned quantities.

Arguments

• ::TurbulenceClosureModel = Struct identifier for turbulence closure model
• orientation = BalanceLaw.orientation
• param_set parameter set
• state = Array of prognostic (state) variables. See vars_state in BalanceLaw
• diffusive = Array of diffusive variables
• aux = Array of auxiliary variables
• t = time

init_aux_turbulence!

Initialise auxiliary variables for turbulence models. Overload for specific turbulence closure type.

principal_invariants(X)

Calculates principal invariants of a tensor X. Returns 3 element tuple containing the invariants.

symmetrize(X)

Given a (3,3) second rank tensor X, compute (X + X')/2, returning a symmetric SHermitianCompact object.

norm2(X)

Given a tensor X, computes X:X.

strain_rate_magnitude(S)

Given the rate-of-strain tensor S, computes its magnitude.